The legendre-tau technique for the determination of a source parameter in a semilinear parabolic equation

Abstract

A numerical procedure for an inverse problem concerning diffusion equation with source control parameter is considered. The proposed method is based on shifted Legendre-tau technique. Our approach consists of reducing the problem to a set of algebraic equations by expanding the approximate solution as a shifted Legendre function with unknown coefficients. The operational matrices of integral and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre functions. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.